Aspects of Differential Geometry V

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Aspects of Differential Geometry V is written by Esteban Calviño-Louzao and published by Springer Nature. It's available with International Standard Book Number or ISBN identification 303102432X (ISBN 10) and 9783031024320 (ISBN 13).

Book V completes the discussion of the first four books by treating in some detail the analytic results in elliptic operator theory used previously. Chapters 16 and 17 provide a treatment of the techniques in Hilbert space, the Fourier transform, and elliptic operator theory necessary to establish the spectral decomposition theorem of a self-adjoint operator of Laplace type and to prove the Hodge Decomposition Theorem that was stated without proof in Book II. In Chapter 18, we treat the de Rham complex and the Dolbeault complex, and discuss spinors. In Chapter 19, we discuss complex geometry and establish the Kodaira Embedding Theorem.